It's not a perfect sight, and now and then you get one that's not quite up to scratch, but in general your observations are fairly normal. .
The windage clicks in particular seem to vary the most from sight to sight and they are not as positive as you'd find on a Garand or M14. On the other hand, I've never had it move when it wasn't supposed to.
The elevation lock screw can be quite secure but it's a matter of pressing the adjustment barrel down against the detent ball, and holding it there while you tighten up the locking collar as much as you can with finger pressure.
Once you establish a zero you can mark one of the lines on the elevation adjustment barrel with paint or white crayon and it will be obvious if it has wandered. It's not a bad idea to note how many turns and clicks up from the bottom it need to be in order to be zeroed, but marking the correct line lets you just worry about number of full turns up from the bottom.
Another option, if the aperture is not overly high over the adjustment barrel and locking collar is to get a larger diameter aperture - one large enough to interfere with the collar when the aperture is screwed all the way in. The interference fit prevents the locking collar and adjustment barrel from turning.
One thing to check for as well is to ensure the allen screw in the base of the sight is securely holding the sight elevator, and that it's maintaining maximum pressure on the detent ball.
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The Lyman No 2 tang sight is not windage adjustable and sight has no clicks at all per se in elevation, just marks on the elevator, so it's infinitely adjustable within it's range but less repeatable. However the lock mechanism is excellent and it's a better choice if you plan to just zero the rifle or carbine and seldom, if ever, change the elevation.
You'll need to adjust windage by either moving the front sight, or if you plan to leave the elevation on one setting, you can shim the base of the sight to tilt it slightly to one side or the other to zero for windage.